So... is Cuticle Tantei Inaba finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: March 22, 2013
Manga finished: March 18, 2017
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
Cuticle Tantei Inaba is a comedic detective series set in a world where human-animal hybrids exist alongside humans. Hiroshi Inaba, a part-wolf detective with a unique ability to glean information from hair, solves crimes that baffle the police. He's aided by his two assistants as he faces off against Don Valentino, a half-goat crime boss with a bizarre taste for money.
The series focuses on Inaba's efforts to stop Valentino's criminal activities, using his unusual skills and overcoming his own eccentricities to bring the villain to justice. Expect a lot of bizarre clues and absurd situations along the way. The central conflict revolves around Inaba's dedicated pursuit of Valentino and his attempts to thwart the Don's money-fueled schemes.